Which equation has the same solution as x^(2)+13 x-20=1 ? (x-6.5)^(2)=63.25 (x-6.5)^(2)=-21.25 (x+6.5)^(2)=63.25 (x+6.5)^(2)=-21.25

Simplify Equation: Simplify the given equation by subtracting 1 from both sides to set it equal to zero. x^2 + 13x - 20 - 1 = 0 x^2 + 13x - 21 = 0Complete the Square: Look for a way to express the given equation as a perfect square if possible. We can try to complete the square by finding a number that, when added and subtracted to the x-term, forms a perfect square trinomial. The coefficient of the x-term is 13, so we take half of it, which is 6.5, and square it to get 42.25. We will add and subtract this number to complete the square. x^2 + 13x + 42.25 - 42.25 - 21 = 0Rewrite and Simplify: Rewrite the equation with the completed square and simplify the constants on the right side. (x + 6.5)^2 - 42.25 - 21 = 0 (x + 6.5)^2 - 63.25 = 0Find Equivalent Equation: Now we need to find an equation that has the same solution as the completed square form of the original equation. We can see that the equation (x + 6.5)^2 = 63.25 has the same solution as the completed square form of the original equation.

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Which equation has the same solution as
x^(2)+13 x-20=1 ?

(x-6.5)^(2)=63.25

(x-6.5)^(2)=-21.25

(x+6.5)^(2)=63.25

(x+6.5)^(2)=-21.25

Which equation has the same solution as $x^{2}+13 x-20=1$ ? $\newline$ $(x-6.5)^{2}=63.25$ $\newline$ $(x-6.5)^{2}=-21.25$ $\newline$ $(x+6.5)^{2}=63.25$ $\newline$ $(x+6.5)^{2}=-21.25$

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Q. Which equation has the same solution as

x^{2}+13 x-20=1

\newline

(x-6.5)^{2}=63.25

\newline

(x-6.5)^{2}=-21.25

\newline

(x+6.5)^{2}=63.25

\newline

(x+6.5)^{2}=-21.25

Simplify Equation: Simplify the given equation by subtracting $1$ from both sides to set it equal to zero. $\newline$ $x^2 + 13x - 20 - 1 = 0$ $\newline$ $x^2 + 13x - 21 = 0$
Complete the Square: Look for a way to express the given equation as a perfect square if possible. We can try to complete the square by finding a number that, when added and subtracted to the $x$ -term, forms a perfect square trinomial. $\newline$ The coefficient of the $x$ -term is $13$ , so we take half of it, which is $6.5$ , and square it to get $42.25$ . We will add and subtract this number to complete the square. $\newline$ $x^2 + 13x + 42.25 - 42.25 - 21 = 0$
Rewrite and Simplify: Rewrite the equation with the completed square and simplify the constants on the right side. $\newline$ $(x + 6.5)^2 - 42.25 - 21 = 0$ $\newline$ $(x + 6.5)^2 - 63.25 = 0$
Find Equivalent Equation: Now we need to find an equation that has the same solution as the completed square form of the original equation. $\newline$ We can see that the equation $(x + 6.5)^2 = 63.25$ has the same solution as the completed square form of the original equation.